Answer :
[tex]\frac{2}{3x} + \frac{4}{x} = \frac{7}{x+1} \\ \\x\neq 0 \ \ and \ \x+1\neq 0 \\ \\x\neq 0 \ \ and \ \x \neq -1[/tex]
[tex]\frac{2 }{3x}+\frac{4}{x} = \frac{7}{x+1} \\\\\ \frac{2+12}{3x} = \frac{7}{x+1} \\ \\\frac{14}{3x} = \frac{7}{x+1}\\ \\14(x+1)=3x\cdot 7[/tex]
[tex]14 x+14=21x \\ \\14=21x-14x \\ \\ 7x=14 \ \ /: 7 \\ \\x=2[/tex]
[tex]\frac{2 }{3x}+\frac{4}{x} = \frac{7}{x+1} \\\\\ \frac{2+12}{3x} = \frac{7}{x+1} \\ \\\frac{14}{3x} = \frac{7}{x+1}\\ \\14(x+1)=3x\cdot 7[/tex]
[tex]14 x+14=21x \\ \\14=21x-14x \\ \\ 7x=14 \ \ /: 7 \\ \\x=2[/tex]
[tex] \frac{2}{3x} + \frac{4}{x} = \frac{7}{x+1} [/tex]
[tex] \frac{2}{3x} + \frac{12}{3x} = \frac{7}{x+1} [/tex]
[tex]\frac{14}{3x} = \frac{7}{x+1} [/tex]
[tex]Cross\ multiply :[/tex]
[tex]14(x+1) = 7 \times 3x[/tex]
[tex]14x+14 = 21x[/tex]
[tex]14x-21x =-14 [/tex]
[tex]-7x =-14 [/tex]
[tex]x = \frac{-14}{-7} [/tex]
[tex]\boxed{x=2}[/tex]
[tex] \frac{2}{3x} + \frac{12}{3x} = \frac{7}{x+1} [/tex]
[tex]\frac{14}{3x} = \frac{7}{x+1} [/tex]
[tex]Cross\ multiply :[/tex]
[tex]14(x+1) = 7 \times 3x[/tex]
[tex]14x+14 = 21x[/tex]
[tex]14x-21x =-14 [/tex]
[tex]-7x =-14 [/tex]
[tex]x = \frac{-14}{-7} [/tex]
[tex]\boxed{x=2}[/tex]
